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Princeton University Press eBooks

Quantum Mechanics for Hamiltonians Defined as Quadratic Forms

Barry Simon A

Published Apr 24, 2015• 435 citations
Publisher

Abstract

This monograph combines a thorough introduction to the mathematical foundations of n-body Schrodinger mechanics with numerous new results. Originally published in 1971. The Princeton Legacy Library uses the latest print-on-demand technology to again make available previously out-of-print books from the distinguished backlist of Princeton University Press. These editions preserve the original texts of these important books while presenting them in durable paperback and hardcover editions. The goal of the Princeton Legacy Library is to vastly increase access to the rich scholarly heritage found in the thousands of books published by Princeton University Press since its founding in 1905.

DOI
10.1515/9781400868834

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Quantum Mechanics

Sara McMurry, Alex Van Someren

From the Publisher: This book provides an introduction to the theoretical foundations of quantum mechanics for students of experimental physics. It is intended as an intermediate text for those who have already completed an introductory course in quantum physics.

•Nov 1, 1993•19 citations
This monograph combines a thorough introduction to the mathematical foundations of n-body Schrodinger mechanics with numerous new results. Originally published in 1971. The Princeton Legacy Library uses the latest print-on-demand technology to again make available previously out-of-print books from the distinguished backlist of Princeton University Press. These editions preserve the original texts of these important books while presenting them in durable paperback and hardcover editions. The goal of the Princeton Legacy Library is to vastly increase access to the rich scholarly heritage found in the thousands of books published by Princeton University Press since its founding in 1905.
Although there are many textbooks that deal with the formal apparatus of quantum mechanics (QM) and its application to standard problems, none take into account the developments in the foundations of the subject which have taken place in the last few decades. There are specialized treatises on various aspects of the foundations of QM, but none that integrate those topics with the standard material. This book aims to remove that unfortunate dichotomy, which has divorced the practical aspects of the subject from the interpretation and broader implications of the theory.The book is intended primarily as a graduate level textbook, but it will also be of interest to physicists and philosophers who study the foundations of QM. Parts of it could be used by senior undergraduates too.
The forty-nine papers collected here illuminate the meaning of quantum theory as it is disclosed in the measurement process. Together with an introduction and a supplemental annotated bibliography, they discuss issues that make quantum theory, overarching principle of twentieth-century physics, appear to many to prefigure a new revolution in science. Originally published in 1983. The Princeton Legacy Library uses the latest print-on-demand technology to again make available previously out-of-print books from the distinguished backlist of Princeton University Press. These editions preserve the original texts of these important books while presenting them in durable paperback and hardcover editions. The goal of the Princeton Legacy Library is to vastly increase access to the rich scholarly heritage found in the thousands of books published by Princeton University Press since its founding in 1905.
Offering a detailed account of the key concepts and mathematical apparatus of quantum mechanics, this textbook is an ideal companion to both undergraduate and graduate courses. The formal and practical aspects of the subject are explained clearly alongside examples of modern applications, providing students with the tools required to thoroughly understand the theory and apply it. The authors provide an intuitive conceptual framework that is grounded in a coherent physical explanation of quantum phenomena, established over decades of teaching and research in quantum mechanics and its foundations. The book's educational value is enhanced by the inclusion of examples and exercises, with solutions available online, and an extensive bibliography is provided. Notes throughout the text provide fascinating context on the tumultuous history of quantum mechanics, the people that developed it, and the questions that still remain at its center. This title is also available as Open Access on Cambridge Core.
A novel interpretation of quantum mechanics, first proposed in brief form by Hugh Everett in 1957, forms the nucleus around which this book has developed. In his interpretation, Dr. Everett denies the existence of a separate classical realm and asserts the propriety of considering a state vector for the whole universe. Because this state vector never collapses, reality as a whole is rigorously deterministic. This reality, which is described jointly by the dynamical variables and the state vector, is not the reality customarily perceived; rather, it is a reality composed of many worlds. By virtue of the temporal development of the dynamical variables, the state vector decomposes naturally into orthogonal vectors, reflecting a continual splitting of the universe into a multitude of mutually unobservable but equally real worlds, in each of which every good measurement has yielded a definite result, and in most of which the familiar statistical quantum laws hold. The volume contains Dr. Everett's short paper from 1957, "'Relative State' Formulation of Quantum Mechanics," and a far longer exposition of his interpretation, entitled "The Theory of the Universal Wave Function," never before published. In addition, other papers by Wheeler, DeWitt, Graham, and Cooper and Van Vechten provide further discussion of the same theme. Together, they constitute virtually the entire world output of scholarly commentary on the Everett interpretation. Originally published in 1973. The Princeton Legacy Library uses the latest print-on-demand technology to again make available previously out-of-print books from the distinguished backlist of Princeton University Press. These editions preserve the original texts of these important books while presenting them in durable paperback and hardcover editions. The goal of the Princeton Legacy Library is to vastly increase access to the rich scholarly heritage found in the thousands of books published by Princeton University Press since its founding in 1905.
Some of the articles in this collection give up-to-date accounts of areas in mathematical physics to which Valentine Bargmann made pioneering contributions. The others treat a selection of the most interesting current topics in the field. The contributions include both reviews and original results. Contents: The Inverse r-Squared Force (Henry D. I. Abarbanel; Certain Hilbert Spaces of Analytic Functions Associated with the Heisenberg Group (Donald Babbitt); Lower Bound for the Ground State Energy of the Schrodinger Equation Using the Sharp Form of Young's Inequality (John F. Barnes, Herm Jan Brascamp, and Elliott II. Lieb); Alternative Theories of Gravitation (Peter G. Bergmann; )Generalized Wronskian Relations (F. Calogero); Old and New Approaches to the Inverse-Scattering Problem (Freeman J. Dyson); A Family of Optimal Conditions for the Absence of Bound States in a Potential (V. Glaser, A. Martin, H. Grosse, and W. Thirring); Spinning Tops in External Fields (Sergio Hojman and Tullio Regge); Measures on the Finite Dimensional Subspaces of a Hilbert Space (Res Jost); The Froissart Bound and Crossing Symmetry (N. N. Khuri); Intertwining Operators for SL(n,R) (A. W. Knapp and E. M. Stein); Inequalities for the Moments of the Eigenvalues of the Schrodinger Hamiltonian and Their Relations to Sobolev Inequalities (Elliott H. Lieb and Walter Thirriny); On the Number of Bound States of Two Body Schrodinger Operators (Barry Simon); Quantum Dynamics: From Automorphism to Hamiltonian (Barry Simon); Semiclassical Analysis Illuminates the Connection between Potential and Bound States and Scattering (John Archibald Wheeler); Instability Phenomena in the External Field Problem for Two Classes of Relativistic Wave Equations (A. S. Wightman) Originally published in 1976. The Princeton Legacy Library uses the latest print-on-demand technology to again make available previously out-of-print books from the distinguished backlist of Princeton University Press. These editions preserve the original texts of these important books while presenting them in durable paperback and hardcover editions. The goal of the Princeton Legacy Library is to vastly increase access to the rich scholarly heritage found in the thousands of books published by Princeton University Press since its founding in 1905.